There will be blood?

For some reason, its believed in the crossfit community that as soon as you walk away from a WOD, with blood all over your hands, shins or anywhere, you've done a GREAT job. How awesome, I'm bleeding everywhere, I'm such a badass! Sure.
Numerous pictures of people showing off their bleeding hands and smiling proudly, to be perfectly honest, is nothing to be proud of.
Ripped hands will need to heal, and that will take time. Ever tried doing a WOD the day after? Exactly.

Woohoo, we're so cool!

Sure, it can happen, but it should never be seen as some sort of badge of honor, at least in our humble opinion. There are ways to prevent such injuries as much as possible, and don't worry, you can still be a bad-ass.

Hands
They are the most common issue, from kipping pull-ups for example, and a proper grip is essential to prevent injuries. People tend to grab the bar in the middle of their palms, causing the skin to squish. Add a bit of friction, and voila, blisters will be guaranteed to appear.

Teach yourself to grab the bar across the bottom of the proximal phalanges (yes, they don't just exist in Friends!) Your skin will be less likely to roll up.
Mark Rippetoe has a simple video regarding the grip here.

Shins

Hitting your shins with anything is just freakin' painful, these is a reason why athletes in other sports wear shin guards. Also, if you are a woman who likes to wear dresses to show off those awesome crossfit legs, it's safe to assume you don't want to show off the bloody scabs and bruises as well. It's ok to be a bit vain sometimes. Or simply take care of your legs, you only have 2 after all.

There are a few solutions for this, the first one being the long socks. Yes, they are made fun of, but after a few SDHP's with a barbell, it's not so funny anymore. Wear them, your skin will thank you.
Another option is a bit odd, at least at first I got a few funny looks when I first tried it, but they soon wore off; Shin guards. For rope-climbs to be more precise.

Even with the best technique, the rope will still scratch your skin, and even though socks might help a bit, there is still friction. I personally scar badly, so decided to give a (soccer) shin guard a try. It works.
The plastic provides just a little bit more protection, making it also easier to make faster rope ascents. Get one that straps under your foot, so it will stay in place.

A few other things to consider:

Too much chalk. Often the first thing people do, is run to the chalk bucket & cover everything in chalk. You really don't need chalk with everything, really. Sure, it can provide a better grip, but it also absorbs all the moisture out of your skin, sometimes causing even more friction. Just think about whether you use chalk because you think you have to or because you need to.

Taping everything (and the wrong way) Tape can again provide protection, or it can work against you. Only tape the areas you have to, and tape properly (so it will last)

Not taking care of calluses. You will get them, whether you like it or not, but grooming them is important. Remove excess skin, it will be less likely to tear. Lotion, pumice stone, callus shavers are all handy tools for that.

Gloves. All the time. We're not a fan of gloves and never will be. It's just more stuff that can cause friction. The end.

Again, injuries can happen, but if there are ways to prevent them as much as possible, then why not?